The present invention relates to devices for screwing caps onto the neck of bottles or similar containers, of the type comprising a screwing head axially movable along a screwing axis and able to rotate about said axis to transmit a rotation to an organ destined to grip the cap, in synchronism with the axial movement of the head, to cause the cap to be screwed onto the bottle, in which said gripping organ has a tubular shape, with an end mouth which is able to receive and grip the cap therein, in which inside each tubular grip organ is mounted in sliding fashion a thruster member, and in which means are provided for controlling the axial position of said thruster member within the grip organ.